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I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!

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Put-call parity says that a call and put (worth $C$ and $P$ respectively) with the same strike $K$ have the following relationship with the spot rate $S$, risk-free rate $r$, and time to maturity $T$ --

$$C - P = S - e^{-rT} K$$

Taking the first derivative with respect to $S$,

$$ \frac{\partial C}{\partial S} - \frac{\partial P}{\partial S} = 1 $$

which relates the delta of the call and put. Taking the second derivative,

$$ \frac{\partial^2 C}{\partial S^2} - \frac{\partial^2 P}{\partial S^2} = 0 $$

which implies that the call and put have the same gamma.

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  • $\begingroup$ LOL it's so easy. Thanks. $\endgroup$ – SPMQET Sep 2 at 14:33

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